Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Modelling Palaeoecological Time Series Using Generalised Additive Models

Abstract: In the absence of annual laminations, time series generated from lake sediments or other similar stratigraphic sequences are irregularly spaced in time, which complicates formal analysis using classical statistical time series models. In lieu, statistical analyses of trends in palaeoenvironmental time series, if done at all, have typically used simpler linear regressions or (non-) parametric correlations with little regard for the violation of assumptions that almost surely occurs due to temporal dependencies in the data or that correlations do not provide estimates of the magnitude of change, just whether or not there is a linear or monotonic trend. Alternative approaches have used LOESS-estimated trends to justify data interpretations or test hypotheses as to the causal factors without considering the inherent subjectivity of the choice of parameters used to achieve the LOESS fit (e.g. span width, degree of polynomial). Generalized additive models (GAMs) are statistical models that can be used to estimate trends as smooth functions of time. Unlike LOESS, GAMs use automatic smoothness selection methods to objectively determine the complexity of the fitted trend, and as formal statistical models, GAMs, allow for potentially complex, non-linear trends, a proper accounting of model uncertainty, and the identification of periods of significant temporal change. Here, I present a consistent and modern approach to the estimation of trends in palaeoenvironmental time series using GAMs, illustrating features of the methodology with two example time series of contrasting complexity; a 150-year bulk organic matter δ15N time series from Small Water, UK, and a 3000-year alkenone record from Braya-So, Greenland. I discuss the underlying mechanics of GAMs that allow them to learn the shape of the trend from the data themselves and how simultaneous confidence intervals and the first derivatives of the trend are used to properly account for model uncertainty and identify periods of change. It is hoped that by using GAMs greater attention is paid to the statistical estimation of trends in palaeoenvironmental time series leading to more a robust and reproducible palaeoscience.

Simplified Spatial Correlation Models for Clustered MIMO Channels With Different Array Configurations

Abstract: An approximate spatial correlation model for clustered multiple-input multiple-output (MIMO) channels is proposed in this paper. The two ingredients for the model are an approximation for uniform linear and circular arrays to avoid numerical integrals and a closed-form expression for the correlation coefficients that is derived for the Laplacian azimuth angle distribution. A new performance metric to compare parametric and nonparametric channel models is proposed and used to show that the proposed model is a good fit to the existing parametric models for low angle spreads (i.e., smaller than 10deg). A computational-complexity analysis shows that the proposed method is a numerically efficient way of generating the spatially correlated MIMO channels.

Robust output tracking for non-linear systems

Abstract: The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(∊), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control te...

Robust Mean-Covariance Solutions for Stochastic Optimization

Abstract: We provide a method for deriving robust solutions to certain stochastic optimization problems, based on mean-covariance information about the distributions underlying the uncertain vector of returns. We prove that for a general class of objective functions, the robust solutions amount to solving a certain deterministic parametric quadratic program. We first prove a general projection property for multivariate distributions with given means and covariances, which reduces our problem to optimizing a univariate mean-variance robust objective. This allows us to use known univariate results in the multidimensional setting, and to add new results in this direction. In particular, we characterize a general class of objective functions (the so-called one- or two-point support functions), for which the robust objective is reduced to a deterministic optimization problem in one variable. Finally, we adapt a result from Geoffrion (1967a) to reduce the main problem to a parametric quadratic program. In particular, our results are true for increasing concave utilities with convex or concave-convex derivatives. Closed-form solutions are obtained for special discontinuous criteria, motivated by bonus- and commission-based incentive schemes for portfolio management. We also investigate a multiproduct pricing application, which motivates extensions of our results for the case of nonnegative and decision-dependent returns.

Nonparametric Discriminant Analysis

Abstract: A nonparametric method of discriminant analysis is proposed. It is based on nonparametric extensions of commonly used scatter matrices. Two advantages result from the use of the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired. This is in contrast to parametric discriminant analysis, which for an L class problem typically can determine at most L 1 features. Second, the nonparametric nature of the scatter matrices allows the procedure to work well even for non-Gaussian data sets. Using the same basic framework, a procedure is proposed to test the structural similarity of two distributions. The procedure works in high-dimensional space. It specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided. The nonparametric scatter matrices are also used to derive a clustering procedure, which is recognized as a k-nearest neighbor version of the nonparametric valley seeking algorithm. The form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm.